Do all these boards use the same type of 32-bit processor? It seems like they can all more or less be programmed by the Arduino IDE. I'm reading about all 3, but I don't understand the differences in how they are programmed. Are the libraries interchangeable?
How would you recommend getting started in 32-bit microcontrollers? Would it make sense to get the Due so I can have Arduino support and then port the code to one of the others if I want to make a permanent project? I do that now with Nano clones. Do real development on an Arduino and then use a $2 Nano clone when I want to make a project.
Yes they can all be programmed in the Arduino IDE if you have the relevant core files for the processor installed.
A potential downside of the 32bit processors are they are 3.3V, though some like the Teensy3 can tolerate 5V signals on some pins but only produce 3.3V signals.
Do all these boards use the same type of 32-bit processor?
Sort-of. As you may know, the "microcontrollers" used on Arduino boards are different from "microprocessors" in that they put most of the relevant components that make up a full computer onto a single chip. The CPU, Flash program memory, static RAM, and peripherals like Timers, UARTs, USB ports, and IO ports are all put together.
Due, Maple, and Teensy 3.x all use an ARM CPU. ARM is an "intellectual property" company that designs mostly JUST the CPU components of a computer. They then license that CPU code to manufacturers (Atmel, ST Microelectronics, and NXP/Freescale) who combine that CPU with their own designs for memory and peripherals, making various decisions about the details, and the manufacturers sell the chips. So Due, Maple, and Teensy all have the same ARM CPU and can use the same compiler (well, Teensy has a "Cortex M4" CPU while the others have "Cortex M3", but they're very similar.) But all of the peripherals are quite different from the different manufacturer, so the Arduino core and various libraries have to be re-written for each one. (Even from the same manufacturer, two different chips can have much different peripherals - the Due and Zero both come from Atmel, but the peripherals are very different!)
Libraries are NOT interchangeable (not peripheral libraries, anyway.)
Since Due is currently not being manufactured by either major "Arduino" Player, and Maple is defunct with HW coming from random China sources, I'd rate the Teensy 3.x as currently being "best supported." (Well, I guess there is also Seeed, which has both Maple and Due clones... Still China, but much less "random.")
I meant "the company." stm32duino.com seems to be doing fine things. But it will depend on how important you think it is to have a company running things...
Teensy isn't [entirely open source]
Only the boot mechanism is proprietary, right? I don't much care. If I want to build a teensy-core-based product, I can load the flash through other methods...